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# Experimental Probability

Experimental probability refers to the probability of an event based on actual experimentation or observation of outcomes.

• Experimental Probability
• Examples
• Formula
• FAQs

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## Experimental Probability

Experimental probability refers to the probability of an event based on actual experimentation or observation of outcomes. It is determined by conducting an experiment or observing an event multiple times and recording the number of times the event occurs.

To find the experimental probability of an event, you would divide the number of times the event occurred by the total number of trials or observations. For example, if you flipped a coin 20 times and it landed on heads 12 times, the experimental probability of flipping heads would be 12/20 or 0.6.

Experimental probability is often used in situations where it is difficult or impossible to determine the theoretical probability of an event. It can be used to estimate the theoretical probability, but it may not be as accurate as using mathematical formulas to calculate probability.

However, experimental probability can still provide valuable information about the likelihood of an event occurring, especially if the sample size is large enough to reduce the effects of randomness and variability.

## Experimental Probability Examples:

Example 1: You roll a six-sided die 100 times and record the number of times each number comes up. You find that the number 3 comes up 23 times. The experimental probability of rolling a 3 on the die is therefore 23/100 or 0.23.

Example 2: You toss a coin 50 times and record the number of times it lands on heads. You find that it lands on heads 27 times. The experimental probability of flipping heads is therefore 27/50 or 0.54.

Example 3: You draw a card from a deck of 52 cards 200 times and record the number of times you draw a heart. You find that you draw a heart 45 times. The experimental probability of drawing a heart is therefore 45/200 or 0.225.

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## Experimental Probability Formula

Here are some common formulas used to calculate probability:

Theoretical Probability Formula: Theoretical probability is the probability of an event based on mathematical calculations. The formula for theoretical probability is:

P(A) = Number of favorable outcomes / Total number of outcomes

where P(A) represents the probability of event A.

Experimental Probability Formula: Experimental probability is the probability of an event based on actual experimentation or observation. The formula for experimental probability is:

P(A) = Number of times event A occurs / Total number of trials or observations

where P(A) represents the probability of event A.

Conditional Probability Formula: Conditional probability is the probability of an event occurring given that another event has already occurred. The formula for conditional probability is:

P(A | B) = P(A and B) / P(B)

where P(A | B) represents the probability of event A given that event B has occurred, P(A and B) represents the probability of both A and B occurring, and P(B) represents the probability of event B occurring.

Multiplication Rule Formula: The multiplication rule is used to calculate the probability of two or more independent events occurring together. The formula for the multiplication rule is:

P(A and B) = P(A) * P(B)

where P(A and B) represents the probability of both A and B occurring, and P(A) and P(B) represent the probabilities of events A and B occurring, respectively.

## Experimental Probability FAQS

##### What is probability?

Probability is a measure of the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

##### What are the types of probability?

There are two main types of probability: theoretical probability and experimental probability. Theoretical probability is based on mathematical calculations, while experimental probability is based on actual experimentation or observation.

##### What is conditional probability?

Conditional probability is the probability of an event occurring given that another event has already occurred. It is calculated using the formula P(A | B) = P(A and B) / P(B), where P(A | B) represents the probability of event A given that event B has occurred.

##### What is the difference between independent and dependent events?

Independent events are events in which the occurrence of one event does not affect the probability of the other event occurring. Dependent events are events in which the occurrence of one event affects the probability of the other event occurring.

##### What is the law of large numbers?

The law of large numbers states that as the number of trials or observations increases, the experimental probability of an event approaches its theoretical probability. This means that with a large enough sample size, the experimental probability becomes more accurate.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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